This thesis covers various applications of topology in condensed matter physics and quantum information. It studies how the topology of the electronic structure of a Weyl semimetal affects the... Show moreThis thesis covers various applications of topology in condensed matter physics and quantum information. It studies how the topology of the electronic structure of a Weyl semimetal affects the transport behaviour of electrons in an applied magnetic field, and how one may employ similar ideas in materials containing Majorana modes to speed up chemistry calculations on a quantum computer. It develops and tests new techniques for decoding topological quantum error correcting codes, in particular for detailed simulation on near-term devices. Finally, it looks towards improving quantum algorithms for future applications in quantum simulation; in particular the classical post-processing of data taken during quantum phase estimation experiments. Show less
Topological superconductors are a novel type of superconductors that carry Majorana particles at their boundary. These surface states are equal superpositions of electrons and holes, and hence are... Show moreTopological superconductors are a novel type of superconductors that carry Majorana particles at their boundary. These surface states are equal superpositions of electrons and holes, and hence are their own anti-particles. There has been a recent surge of theoretical and experimental effort to realize these special particles in the lab. While first observations support the theoretical predictions, fail-safe experimental evidence for Majoranas is still needed. Part of the challenge is that due to their vanishing charge they are not easily detected electrically. The topic of this thesis is the proposal and study of electrical signatures of Majoranas that are present in spite of their charge neutrality. By applying scattering and random matrix theory we first examine their generic properties. With the tool of numerical simulations we then put our predictions to test on realistic systems. Show less
The research contained in this thesis lies at the interface between quantum phyiscs, nanotechnology and the theory of computation. Its goal is to design electronic circuits to realize computations... Show moreThe research contained in this thesis lies at the interface between quantum phyiscs, nanotechnology and the theory of computation. Its goal is to design electronic circuits to realize computations that follow the laws of quantum mechanics, and which would allow to execute some algorithms faster than their classical counterparts - for instance, algorithms to solve chemical problems. In particular, these circuits use Majorana modes, very special states which appear in superconductors and are theoretically predicted to protect information from the environment, so that the computation can be executed without errors. The role of my research was to design electronic circuits able to use this fascinating property. Hence, this work is a bridge between some very abstract mathematical ideas and the very concrete world of electronic circuits, made out of inductors and capacitors. Show less
